Unlike some GGA functionals that yield qualitatively different radial distribution functions for hydroxide, [1]}
the SCAN functional yields a \(\rm g(r)\)  similar to that predicted by PBE0-TS, as shown in Fig. REF .
Regarding the computational costs, SCAN takes the advantage of being much more efficient than the hybrid functional. [2]}
Therefore, it is valuable to compare properties of hydroxide and hydronium
in detail as obtained from the two functionals and we have the following findings.
First, the hydrophobic sites of the two ions are investigated.
We observe a less hydrophobic end in hydroxide (hydrogen site) as compared to that in hydronium (oxygen site),
because the first and the second peaks of \(\rm g_{H^{*}O^{w}}(r)\)  for hydroxide in Fig. REF (a) are considerably
higher than those in the \(\rm g_{O^{*}H^{w}}(r)\)  for hydronium shown in Fig. REF (f), suggesting more water molecules locate around the hydrogen site of hydroxide than the oxygen site of hydronium.
When comparing the results from SCAN to those from PBE0-TS, the hydrophobic site of hydroxide, i.e.,
the hydrogen of hydroxide, becomes less hydrophobic by donating slightly more HBs to its neighbors.
This is evidenced as SCAN yields a higher first peak of \(\rm g_{H^{*}O^{w}}(r)\)  than PBE0-TS in Fig. REF (a).
The result is also consistent with the HB data shown in Fig. REF , where the averaged number of donating HBs in hydroxide is 0.577 and 0.471 from SCAN and PBE0-TS, respectively.
On the contrary, the hydrophobic site of hydronium, i.e., the oxygen site, becomes more hydrophobic by adopting the SCAN functional, which is evidenced by a lower first peak of \(\rm g_{O^{*}H^{w}} (r)\)  located around 3 Å in Fig. REF (f).
Moreover, the peak locates further away from the central atom than the one from PBE0-TS, suggesting that it would be more difficult for hydronium to accept HBs in SCAN (0.138) than in PBE0-TS (0.140), as listed in Fig. REF .
